Factor r^3-64

Problem

r^3−64

Solution

1. Identify the expression as a difference of cubes, which follows the form a^3−b^3

2. Determine the values of a and b by taking the cube roots of each term.

3. Substitute a=r and b=4 into the difference of cubes formula: a^3−b^3=(a−b)*(a^2+a*b+b^2)

4. Simplify the resulting terms within the parentheses.

Final Answer

r^3−64=(r−4)*(r^2+4*r+16)

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